
The order parameter and the slowly varying field operator can be expanded as
[1]}
\(&\Delta ({\mathbf {x}},{\mathbf {R}}) = \Delta ({\mathbf {x}},{\mathbf {r}}-\frac{{\mathbf {x}}}{2}) \simeq \Delta ({\mathbf {x}},{\mathbf {r}}) - \frac{{\mathbf {x}}}{2}\cdot \nabla \Delta ({\mathbf {x}},{\mathbf {r}}) + \cdots , \cr &\psi _{\mathbf {k}_{\rm F}}({\mathbf {r}}^{\prime }) = \psi _{\mathbf {k}_{\rm F}}({\mathbf {r}}-{\mathbf {x}}) \simeq \psi _{\mathbf {k}_{\rm F}}({\mathbf {r}}) - {\mathbf {x}}\cdot \nabla \psi _{\mathbf {k}_{\rm F}}({\mathbf {r}}) + \cdots .\) 
